Formation density measurements are typically used to calculate formation porosity. Using the formation porosity and other measured values, e.g., formation resistivity, an oil or gas well may be evaluated. Furthermore, porosity information concerning a reservoir permits the estimation of other useful determinations, such as the number of recoverable barrels of oil. With such information, accurate decisions by the oil recovery operator may be made concerning the development or production of the reservoir.
Density logging is based on the detection of attenuated gamma rays emitted from a radioactive source. After gamma rays from the source penetrate the borehole and formation, a fraction of the scattered gamma rays are counted by the gamma ray detectors. The scattering which the gamma rays experience after emission from the source and prior to detection is related to formation bulk density. More specifically, the number of gamma rays so scattered is exponentially related to the formation electron density. Since nuclear emission from a radioactive source is random but probabilistic in occurrence, the average count rate must be taken over a period of time long enough to obtain a number of counts sufficient for a statistically accurate count rate measurement.
Formation density measurements made during wireline logging operations by pulling a density tool through a borehole via an electric wireline have been available for decades. In these operations, a density tool which contains a radioactive gamma ray source and typically two gamma ray detectors may be decentralized in the borehole so the detectors directly engage the borehole wall. If the detectors are offset from the borewall, the drilling mud has a severe perturbative effect on the measurement. Typically, a backup arm or spring applies a decentralizing force to the tool for this purpose. To get an accurate measurement, the decentralized logging tool is preferably pulled through the borehole at a speed low enough to allow compensation for count rate statistics, e.g., 0.5 ft/sec.
Despite the decentralizing force, the tool may be displaced from the borewall by a mud cake that often builds up on a permeable formation. To correct for this commonly occurring situation, count rate measurements from the detector closest to the source (the short space detector) and from the furthest detector (the long space detector) are combined to provide a more accurate reading. For this purpose, a spine and rib plot may be used which plots long space and short space count rates against each other for different calibration materials and for different stand-offs between the detectors and the formation.
More recently, measurement while drilling (MWD) tools have been used for making formation density measurements. Density tool electronics and the gamma detectors (both the short space and long space detector) may be disposed in a stabilizer blade affixed to a drill collar in a lower portion of the drill string near the drill bit. The stabilizer blade displaces drilling mud in the annulus of the borehole and places low density windows, installed radially outward of the radiation source and detectors, in contact with the earth formation. During rotary drilling, the MWD tool may typically rotate at a rate of as much as one or two revolutions per second. To account for statistics, data sampling times in the MWD tool are longer than those used with wireline density tools, and are typically in the range of about 30 seconds.
While drilling, contact of the stabilizer blade with the borehole wall may be lost. If the borehole stabilizer blades are the same diameter as the well bore, then wall contact can be assumed to be constant during the 30 second sampling time period. However, it is well known that boreholes are often significantly larger than bit size, and that this enlargement may occur simultaneous with or very soon after passage of the drill bit. This loss of contact affects the density measurement, so that the apparent density detected is greater or less than the true density, depending on the relative densities of the borehole fluid and the formation.
If borehole enlargement has occurred by the time the MWD tool logs the hole, then a measurement taken over a period of 30 seconds can generally be expected to include data from all possible offset distances of the stabilizer blade from the borehole wall. This introduces error into the typical compensation technique which compares the computed density response of the short and long spaced detectors. During the sampling period, count rates are accumulated in a linear fashion for the various borehole offsets experienced during the measurement. However, the response of the tool to the offset distance between the borehole wall and the tool sensors is logarithmic. Therefore, the compensated response of the tool to borehole enlargement will be progressively in error as the borehole size increases. Various methods have been developed which attempt to address these problems.
U.S. Pat. No. 5,017,778 to P. D. Wraight discloses a method and apparatus for determining the mean of successive measurements preferably taken at least twice as fast as drilling RPM, as well as the standard deviation of the successive measurements. These computations are combined for providing output signals in accord with variations in the transverse cross-sectional configuration of the borehole, and provide indications representative of the desired formation characteristic as well as the borehole configuration. This method relies on the theoretical relationship between the mean and the standard deviation under circumstances where there is constant tool contact with the borehole wall. Under these circumstances, the theoretical value of the standard deviation will be substantially the same as the measured standard deviation. However, if the hole is large in diameter such that tool contact with the borehole wall varies, the relationship between tool offset and count rates causes a divergence between the measured standard deviation and its theoretical value. A correction is applied to the mean count rate based on the difference between the measured and theoretical standard deviations.
Because the correction applied to the mean is derived from the standard deviation of the successive measurements, the accuracy of the method depends on the symmetry of the actual distribution of the samples about the mean. To the extent the actual distribution is skewed about the mean, the accuracy of the correction will deteriorate. There are several factors which tend to make the count rate distribution asymmetric about the mean. For instance, it is not uncommon for stable, dynamic situations to be set up for a wide range of combinations of RPM and weight-on-bit, where the tool axis itself will be moving. This movement is often in the form of a repeatable pattern in the hole, and may significantly affect the distribution of successive measurements about the mean. In such a case, depending on the type and extent of "whirling" or movement of the tool axis itself, it is conceivable that the complete circumference of the borehole may not even be scanned at least once during a total sampling period, as required by the Wraight method to assure that meaningful output data is obtained. It is currently difficult to control these situations in real time without the presence of additional downhole sensors, because their occurrence may not be detectable by surface measurements.
Another factor which may cause a skewed distribution of data involves the fact that the effect of density on gamma ray count rate is highly non-linear. For instance, if the tool remains on the "low" side of an elliptical hole, the tool will contact the bore wall for a longer period of time than if the tool remains on the "low" side of a circular hole. Due to the highly non-linear effect on count rate, the distribution of the successive measurements will be skewed.
U.S. Pat. No. 5,091,644 to D. C. Minette discloses a method for analyzing data from a measurement-while-drilling formation evaluation tool to compensate for rotation of the logging tool. The received signal is broken down, preferably into four sections. As the tool rotates, the detectors quickly pass through these four quadrants. Each time they pass a boundary, a counter is incremented, pointing to the next quadrant. Thus, the data is divided into four spectra each obtained for one-fourth of the total acquisition time. To determine the sector in which the tool is operating, the output from a supplementary sensor is used, such as an inclinometer or a magnetometer. Minette also states that an acoustic borehole caliper may be used to divide the borehole into these sections (e.g. quadrants) based on standoff in those sections.
If the tool is centered in a perfectly circular hole, the offset the tool experiences while in each sector will be the same and the number of counts accumulated in each sector will be the same. However, if the tool axis is not aligned with the bore hole axis, this will not be true, and the offset will be different for different sectors. The counts accumulated in each sector will thus be different, with the counts in the sector or sectors corresponding to the minimum offset value being those of highest quality for determination of the formation density.
Like the Wraight description, there is an implicit assumption in the Minette technique that the axis of the tool remains in a fixed orientation in the hole during the measurement. There is, however, no easy and reliable mechanism to keep the tool axis at a fixed location in the borehole. It is thus highly probable that movement of the tool axis about the bore hole will occur in a vertical or near vertical hole. The possibility of such movement never completely disappears, even in a highly deviated hole. Moreover, due to the location of the density sensors in a blade portion of the tool, there may be an increased likelihood of such movement of the tool axis as the blade engages the borehole wall.
Because the sectors or quadrants are assumed to be fixed in the hole, the consequence of axial movement or translation is that there will be less than optimum correlation, or possibly no correlation at all, between sectors that are anticipated to be consistent and tool offset. While use of an acoustic caliper signal to sort the signal into bins based on averaged strand-off may alleviate the problem to some extent, there is still a problem of storing data for the correct quadrant when it is assumed the sectors will arrive consistently and sequentially. During movement of tool axis, the same tool position associated with sectors and quadrants will not necessarily occur consistently and sequentially. Thus, if there is no override to the sequential storing of data, data may be skewed when the tool axis is not fixed, even when using an acoustic caliper sorting signal.
In another method directed to wireline logging with a single detector density tool, U.S. Pat. No. 3,321,627 to C. W. Tittle discloses a collimated source and detector arrangement for a single detector density tool. The collimation concept disclosed in this patent prevents the measurement from being influenced by borehole fluids by collimating the source and detector so that gamma rays are more likely to be directed into the formation. The tool has a source collimator for directing a small solid angle beam of gamma-rays into the material undergoing the density determination. The tool also has a detector collimator for limiting the access of gamma-rays to the gamma-ray detector to those gamma-rays that scatter and travel within a small solid angle that intersect within the formation with the small solid angle beam of gamma-rays from the source. A 1985 Hearst and Nelson article entitled Well Logging for Physical Properties discusses the related concepts of density measurements, and especially single scattering density measurements.
There remains the need for an improved method and apparatus to more accurately measure radiation in a well bore environment that overcomes the problems encountered by prior art tools taking such measurements, including poor accuracy for readings taken at varying standoffs from a borehole wall. Those skilled in the art have long sought and will appreciate the present invention, which provides solutions that substantially alleviate these and other problems.